Abstract

A complicating factor in the translational pharmacology of sphingosine 1-phosphate agonists is that they exert their pharmacological effect through their respective phosphate metabolites, which are formed by the enzyme sphingosine kinase (S1PHK). In this investigation, we present a semimechanistic pharmacokinetic model for the interconversion of S1PHK substrates and their respective phosphates in rats and humans with the aim of investigating whether characterization of the rate of phosphorylation in blood platelets constitutes a basis for interspecies scaling using fingolimod as a model compound. Data on the time course of fingolimod and fingolimod-phosphate (fingolimod-P) blood concentrations after intravenous and oral administration of fingolimod and/or fingolimod-P in rats and after oral administration of fingolimod in doses of 0.5, 1.25, and 5 mg once daily in healthy volunteers were analyzed in conjunction with data on the ex vivo interconversion and blood-plasma distribution in rat and human blood, respectively. Integrating the data from the ex vivo and in vivo studies enabled simulation of fingolimod and fingolimod-P concentrations in plasma rather than blood, which are more relevant for characterizing drug effects. Large interspecies differences in the rate of phosphorylation between rats and humans were quantified. In human, phosphorylation of fingolimod in the platelets was four times slower compared with rat, whereas the dephosphorylation rates were comparable in both species. This partly explained the 10–12-fold overprediction of fingolimod-P exposure in human when applying a dose-by-factor approach on the developed rat model. Additionally, differences in presystemic phosphorylation should also be taken into account.

Introduction

Fingolimod [2-amino-2-[2-(4-octylphenyl)ethyl]propane-1,3-diol; FTY720] is a sphingosine 1-phosphate (S1P) receptor modulator that is effective in the treatment of multiple sclerosis (Cohen et al., 2010). The active metabolite of fingolimod, fingolimod-phosphate (fingolimod-P) binds to 4 of the 5 subtypes of the S1P receptor (S1P1 and S1P3–5) with high affinity (0.3–3.1 nM) (Mandala et al., 2002; Brinkmann et al., 2004; Brinkmann, 2007; Chun and Hartung, 2010). In contrast, the affinity of fingolimod for all S1P receptors is low (Hale et al., 2004; Albert et al., 2005). Phosphorylation of fingolimod is therefore a critical step in its pharmacological effect. With the discovery of fingolimod and the elucidation of its mechanism of action, the search for other S1P agonists with different pharmacokinetic (PK)-pharmacodynamic properties has been propelled. Currently available S1P agonists can be categorized into two classes: amino alcohol prodrugs and second-generation direct agonists (Cusack and Stoffel, 2010). The first class of compounds, to which fingolimod belongs, owes it biologic activity to phosphorylation by the enzyme sphingosine kinase (S1PHK) (Billich et al., 2003; Kharel et al., 2005; Kihara and Igarashi, 2008). There are important interspecies differences in the expression and function of S1PHK. In the rat, S1PHK is predominately expressed in the kidney, spleen, and liver tissue (Olivera et al., 1998). In humans, S1PHK1, which is one of the two S1PHK isoforms, is mainly expressed in lung and spleen, whereas the other isoform, S1PHK2, is predominantly expressed in liver and heart tissue (Liu et al., 2000; Paugh et al., 2003). These large interspecies differences complicate the prediction of exposure to phosphorylated S1P prodrugs in humans using in vivo animal data. Therefore, an allometric scaling approach, which does not consider interspecies differences in enzyme tissue distribution or enzyme activity, will not be applicable to S1P prodrugs. Because an adequate characterization of the exposure in rat and human may be important for translational modeling (Danhof et al., 2008),] a qualitative and quantitative understanding of differences in the PK of S1PHK substrates between rat and human must be considered.

Fingolimod is an interesting model compound to investigate the pharmacokinetics of S1PHK substrates, because the interconversion between fingolimod and its phosphate has been well investigated in several in vitro, in vivo, and ex vivo studies (Olivera et al., 1998; Liu et al., 2000; Billich et al., 2003; Albert et al., 2005; Kovarik et al., 2007; Kihara and Igarashi, 2008). From ex vivo studies it is known that fingolimod is phosphorylated in the blood platelets (Albert et al., 2005; Anada et al., 2007; Kihara and Igarashi, 2008). We hypothesize that characterization of the interconversion between fingolimod and fingolimod-P in blood platelets may constitute a basis for the scaling of the PK between rats and humans. To date, no PK models have been published that describe the time course of the fingolimod and fingolimod-P concentrations simultaneously. Because the conversion between fingolimod and its phosphate is a reversible and dynamic process it is anticipated that the PK of fingolimod-P is closely linked to the PK of fingolimod. Therefore, a simultaneous analysis of the in vivo concentration-time course of fingolimod and fingolimod-P and the ex vivo interconversion and blood-plasma distribution will yield an understanding of the dynamics of the overall interconversion and the relevance of the interconversion in blood platelets. Moreover, characterizing the blood to plasma distribution allows the simulation of the fingolimod-P plasma concentrations rather than whole blood concentrations, which are the relevant concentrations for the modeling of pharmacodynamic effects in future pharmacokinetic pharmacodynamic investigations.

In this investigation, we present a semimechanistic population PK model for the interconversion of S1PHK substrates and their respective phosphates using fingolimod as a model compound with the aim 1) to investigate whether characterization of the interconversion in blood (platelets) constitutes a basis for the scaling of the PK between rats and humans and 2) to simulate the time course of plasma (rather than whole blood) concentrations of phosphate metabolites.

Materials and Methods

An overview of the studies used to characterize the PK of fingolimod(-P) in rat and human can be found in Table 1.

Ex Vivo Studies.

Three ex vivo experiments were performed in isolated blood from male albino rats of strain Hanover Wistar and human blood obtained from healthy male volunteers (Blutspendezentrum SRK, Basel, Switzerland). Experiment A was an interconversion experiment in which (rat and human) blood samples (∼6 ml) were spiked with a fingolimod or fingolimod-P spiking solution [20 µg/ml; solvent: ethanol abs: 1 M HCl (95:5, w/w)] to achieve final concentrations of 100 ng/ml fingolimod and fingolimod-P. In total, 11 samples were incubated at 37°C with gentle agitation. Aliquots (0.8 ml) were taken after 0, 1, 2, 4, 7, 24, and 48 hours of incubation, immediately frozen on dry ice, and stored at −80°C. Fingolimod and fingolimod-P blood concentrations were determined by liquid chromatography tandem mass spectrometry after liquid/liquid extraction. The lower limits of quantification (LOQ) were 1.08 and 2.5 ng/ml for fingolimod and fingolimod-P, respectively. Experiments B and C investigated the blood/plasma distribution of fingolimod-P. In experiment B, the time dependency of blood/plasma distribution (time points: 0.25, 0.5, 1, 2, and 4 hours) was studied for a concentration of 30 ng/ml [14C]fingolimod-P in rat blood and at 30 and 300 ng/ml [14C]fingolimod-P in human blood. Experiment C investigated the fingolimod-P blood/plasma distribution for the nominal concentrations of 3, 30, 300, and 3000 ng/ml [14C]fingolimod-P in triplicate (in addition at 1 and 0.3 ng/ml for human). Samples were incubated for 120 minutes at 37°C with constant agitation on an orbital shaker. In experiments B and C, separation of cells and plasma was achieved by centrifugation (1500 g, 10 minutes, 37°C). Samples for quantification of total radioactivity were taken before and after (plasma fraction only) centrifugation. The radioactivity in the biologic samples was measured by liquid scintillation counting with Irga-Safe Plus (Packard Instrument Co., Meriden, CT) as scintillator. Radiometry was performed in TriCarb 2500 TR and 2700 TR Liquid Scintillation Systems (Packard). Concentrations of radiolabeled substances in plasma and blood were determined in weighed samples. Data were converted from disintegrations per minute per gram to nanograms per milliliter, assuming a density of 1.00 g/ml for all samples and using the specific radioactivity.

Studies in Rat.

The studies in rats were conducted in accordance with the Guide for the Care and Use of Laboratory Animals as adopted and promulgated by the U.S. National Institutes of Health (Bethesda, MD).

Study 1 was a single dose PK study in which fingolimod and fingolimod-P concentrations where measured after intravenous and oral administration of fingolimod in male Lewis rats. Rats were provided normal chow and water ad libitum. Study 2 was a study on the PK of fingolimod and fingolimod-P after single intravenous administration of fingolimod or fingolimod-P in male Sprague-Dawley rats (Charles River, L'Arbresle, France). At the time of study, body weights ranged from 296 to 318 g. Rats were provided normal chow (NAFAG pellets No. 890, ECOSAN Eberle NAFAG AG, Gossau, Switzerland) and tap water ad libitum. In these pharmacokinetic investigations the vena femoralis was cannulated for compound administration and the arteria femoralis for blood sample collection. After cannulation, a recovery period of 72 hours was observed. Meloxicam was used for postsurgery analgesia (1–2 mg/kg, s.c.). Cannulae were filled with aqueous heparin solution. During the recovery time, the functional capability of the cannulae was regularly tested.

Studies in Healthy Volunteers.

Studies in healthy volunteers were conducted in accordance with the Declaration of Helsinki. The protocols for studies 2105, 2213, and 2215 were approved by local medical ethics committees, and written informed consent was obtained from all subjects. Subjects were judged eligible for the studies if they were aged between 19 and 50 years or between 18 and 45 years for studies 2105 and 2213/2215, respectively. In addition, all subjects were in good health as determined by past medical history, physical examination, vital signs, electrocardiogram, and laboratory tests at screening.

Bioanalytics.

Venous blood samples were collected according to the sampling schemes described in Table 1. Blood concentrations were determined by a validated liquid chromatography method with mass spectrometry detection. Samples were analyzed after liquid-liquid extraction (Kovarik et al., 2004). In the studies in rats, the LOQs were 0.250 and 1 ng/ml for fingolimod and fingolimod-P, respectively. In the clinical studies the LOQ was 0.080 ng/ml for fingolimod. For fingolimod-P, the LOQs were and 0.1 and 1 ng/ml in studies 2105 and 2215, respectively. Assay accuracy ranged from 97.5 to 108.7% and precision coefficients of variation from −2.5 to 8.7%.

Population PK Modeling Strategy.

Two PK models were developed, i.e., one model to characterize the PK of fingolimod and fingolimod-P in rat and one model to characterize the PK of fingolimod and fingolimod-P in human. The rat PK model was developed using data from studies 1 and 2 and the ex vivo studies in rat blood. Data from all ex vivo and in vivo studies were analyzed simultaneously while taking into account the time course of the interconversion between fingolimod and fingolimod-P and the blood-plasma distribution. In addition, the fact that these processes also occur in the isolated blood was accounted for. The human PK model was developed using data from studies 2105 and 2213 and the ex vivo studies in human blood. Data from study 2215 were used for (external) evaluation of the predictive value of the model.

Only physiologically plausible models were evaluated, i.e., all evaluated models were based on the knowledge from published in vitro, in vivo, and ex vivo studies. Briefly, the following is known about the interconversion between fingolimod and its phosphate.

Fingolimod-P is dephosphorylated back to fingolimod before it is eliminated from the body (Zollinger et al., 2011).

Dephosphorylation occurs only in the plasma. Fingolimod-P is dephosphorylated by the enzyme lipid phosphatase type 3 (Kihara and Igarashi, 2008), which is expressed in the plasma membrane on cells exposed to plasma such as vascular endothelial cells and blood cells (Kihara and Igarashi, 2008).

One-, two-, and three-compartmental models were evaluated to describe the disposition of fingolimod and fingolimod-P. Furthermore, it was investigated if the absorption from the gastrointestinal tract (dose compartment) to the blood (central compartment) could be described with first- or zero-order processes. In addition, an exploratory graphical analysis of the dose-normalized raw fingolimod and fingolimod-P blood concentrations indicated that absorption, distribution, and/or interconversion might be nonlinear with dose/concentration. Therefore, it was evaluated if the description of the data could be improved by describing the absorption, distribution, or interconversion by saturable processes, i.e., by Michaelis-Menten-like processes (eq. 1) or by saturable binding to plasma proteins (eq. 2):

(1)

In this equation A(x) is the amount in compartment x, C(x) is the concentration in compartment x, Vm is the maximum rate of biotransformation and Km is the concentration at which the half maximal rate of biotransformation is reached. The term SPK is used to represent saturation of a certain mechanism, e.g., a saturable distribution or saturable interconversion. It results in a sigmoid relationship approaching a maximum at infinitely high concentration.

(2)

In case of saturable binding, in this equation, phi is the free fraction, C is the total concentration in the plasma and Bmax and Kd are the binding capacity and binding affinity, respectively.

Computation.

Data from the in vivo and ex vivo studies were analyzed simultaneously using the nonlinear mixed-effects modeling approach implemented in NONMEM (version 7.1.0; Icon Development Solutions, Ellicott City, MD). The models were compiled using Digital Fortran (version 6.6C3, Compaq Computer Corporation, Houston, TX) and executed on a personal computer equipped with an AMD Athlon 64 processor 3200+ under Windows XP. The results were analyzed using the statistical software package S-Plus for Windows (version 6.2 Professional, Insightful Corp., Seattle, WA). Parameters were estimated using the first-order conditional estimation method with interaction between the two levels of stochastic effects (FOCE interaction). Random effects were included as exponential terms reflecting lognormal distributions of model parameters. The residual variability was explored with proportional and additive error models. Goodness-of-fit was determined using the minimum value of the objective function defined as minus twice the log-likelihood. For nested models, a decrease of 10.8 points in the minimum value of the objective function (corresponding to P < 0.001 in a χ2 distribution) by adding an additional parameter was considered significant. The goodness-of fit was also investigated by visual inspection of the plots of individual predictions and the diagnostic plots of (weighted) residuals. To evaluate the predictive value of the human pharmacokinetic model, a visual predictive check was performed in which the median and the 90% interquantile range of data simulated with the developed model were plotted together with the observations. In addition, the predictive value of the human pharmacokinetic model was externally validated with data from study 2215 using the same visual predictive check technique.

Results

Rat PK Model.

The data from the rat ex vivo and in vivo studies (studies 1 and 2) were described by the model depicted in Fig. 1 (rat) and specified in Appendix 1. Phosphorylation of fingolimod was described by the combination of a first-order process in the platelets (k67) and a first-order phosphorylation process in plasma (k34), which is only relevant in vivo. In vivo dephosphorylation was found to be faster than the ex vivo dephosphorylation. This was accounted for by estimating an extra rate constant (k43b), which is only relevant in vivo. The disposition of fingolimod and fingolimod-P was characterized by three-compartmental models with saturable distribution from the plasma to one of the peripheral compartments for fingolimod and fingolimod-P. Absorption and elimination of fingolimod were described by first-order processes (absorption rate constant and k30). The total bioavailability was found to be dose dependent to decrease from 1, for a dose of 0.1 mg/kg, to 0.36, for the highest orally administered dose, i.e., 3 mg/kg, according to a descriptive log-dose equation (Table 2), which is only valid in the observed dose range between 0.1 and 3 mg/kg. Fingolimod was also presystemically phosphorylated. As calculated from the absorption rates, 82% of the total bioavailable fingolimod dose was converted into fingolimod-P before entering the systemic blood. Absorption of the presystemically formed fingolimod-P was characterized by two transit compartments to describe observed delay in absorption. In addition, the absorption from the last transit compartment to the central compartment was described by a saturable Michaelis-Menten-like process. The ex vivo blood volume and in vivo central volume of distribution were allowed to vary between experiments and between individual rats (IIV). The residual errors for the ex vivo and in vivo were best described by proportional residual error models with an extra additive residual error for ex vivo experiment A.

Pharmacokinetic models to describe the time course of the fingolimod and fingolimod-P blood concentration in rat and human. The gray area describes the interconversion and blood/plasma distribution in isolated blood. Kxy represents the first-order distribution and elimination rate constants. Arrows with an equal number of slashes indicate that these rates are the same. In addition, the dashed lines represent saturable processes.

The parameter values from the PK models to describe the time course of the fingolimod and fingolimod (-P) blood concentrations in rat and human

The developed model adequately described the interconversion between fingolimod and fingolimod-P as well as the blood-plasma distribution as can be seen in the description of the data from the ex vivo experiments (Fig. 2, rat). The in vivo time course of the fingolimod (-P) blood concentrations was also adequately described after both intravenous and oral administration of fingolimod (Fig. 3). To evaluate if the data were informative for estimation of the blood-specific parameters including the rate of phosphorylation (k67), a retrospective sensitivity analysis was performed, using the parameter estimates of the developed model (Appendix 3). This sensitivity analysis demonstrated that the combined data of the ex vivo and in vivo studies provided the pertinent information to quantify the blood-specific parameters. All structural parameters could be estimated with good precision, because all standard errors were less than 50% of the parameter estimates (Table 2). In addition, all parameter correlations were below 0.95. The estimated clearance of 0.774 l/h per kg does not differ from the systemic clearance of 0.748 l/h per kg derived from a published physiologically based pharmacokinetic (PBPK) model (Meno-Tetang et al., 2006).

Description of the data from the ex vivo interconversion (A) and blood/plasma distribution (B and C) studies in isolated blood from rat (top) and human (bottom). The dots represent the observations, and the continuous lines (A and B) and squares (C) represent the individual predictions. The dashed lines represent the population predictions.

Description of the fingolimod and fingolimod-P blood concentrations from studies 1 and 2 after oral fingolimod (dose: 0.1, 0.3, 1, or 3 mg/kg) or intravenous administration of fingolimod (dose: 1 mg/kg) or fingolimod-P (dose: 0.1 mg/kg). The gray dots represent the observations and the dashed lines represent the population predictions.

Human PK Model.

The model to describe the data from the human ex vivo and in vivo studies (studies 2213 and 2105) was comparable to the model to describe the rat data (Fig. 1, human; Appendix 2). However, several differences are noticeable between the rat and human models. 1) Only one peripheral compartment could be quantified to describe the distribution of fingolimod-P. 2) The phosphorylation and dephosphorylation processes in plasma, which were identified in rat, could not be quantified in human. Instead, the dephosphorylation in plasma was described by a saturable, Michaelis-Menten-like process (eq. 1). 3) In human, two peaks were observed during the absorption phase. This was described by two dose compartments with a lag time for the absorption from the second dose compartment. 4) The distribution of fingolimod into the red blood cells could be quantified in human, whereas this process could not be quantified in rat. 5) The distribution of fingolimod-P into the platelets and the peripheral compartment was found to be faster for higher concentrations. This was described by a saturable binding process (eq. 2) resulting in a higher blood/plasma ratio for higher concentrations (Fig. 2C, human). k30 and the in vivo blood volume were allowed to vary between individual subjects. The residual errors for the ex vivo and in vivo studies were best described by proportional residual error models.

In general, the developed model adequately described the data from the ex vivo studies (Fig. 2, human). In addition, the time course of the in vivo fingolimod and fingolimod-P blood concentrations was adequately described as the continuous lines, which represent the predicted median, closely resemble the observed median (dashed lines) (Fig. 4). However, the observations from the 1.25-mg dose group in study 2105 were slightly overpredicted. For study 2213, the variability was adequately predicted as about 90% of the observations are within the 90% prediction interval (Fig. 4, gray area). For study 2105, the variability was slightly overpredicted. All parameters could be estimated with good precision, because all standard errors were less than 50% of the parameter estimates (Table 2). About 69% of the total fingolimod dose was converted to fingolimod-P before entering the blood. A comparison of the time course of the simulated fingolimod-P blood and plasma concentrations demonstrates that for a dose of 0.5 mg/day the fingolimod-P blood/plasma concentration ratio varies between 0.8 and 0.95 within a day at steady state. The difference between blood and plasma concentrations is the largest around the time at which the maximum plasma concentration is reached (Fig. 5).

Visual predictive check of the description of the fingolimod and fingolimod-P blood concentrations from multiple-dose studies 2105 and 2213 in health volunteers. The gray dots represent the observations after administration of fingolimod (0.5, 1.25, or 5 mg by mouth) and the dashed lines represent the observed median. The continuous lines represent the predicted median and the gray area represents the 90% prediction interval.

Predicted fingolimod-P blood and plasma concentrations and blood/plasma ratio after once daily administration of fingolimod during 14 days. The gray line represents the predicted fingolimod-P plasma concentration, and the dashed black lines represent the predicted fingolimod-P blood concentration after administration of fingolimod (0.5 mg by mouth). The dashed gray lines represents the predicted blood/plasma ratio.

The developed model could, in general, adequately predict both the trend and the variability in the data from the external (i.e., study not used for model development) study 2215 (see Supplemental Fig. S). However, fingolimod and fingolimod-P concentrations observed in the 10 mg–dose group were slightly overpredicted. On the other hand, the concentrations of 5 out of 6 subjects included in this treatment group fall within the prediction interval. Therefore, this might be a chance observation, which is due to the low number of subjects. The observed concentrations of the 6th subject of this treatment are much lower than predicted but also much lower than the observed concentrations in the lowest dose group. In addition, the maximum fingolimod-P concentrations are slightly underpredicted for the higher dose groups. This indicates that there might be another nonlinear process involved that becomes relevant after administration of doses higher than 10 mg.

Comparison of Exposure between Rat and Human.

A comparison between the predicted steady-state fingolimod-P exposure in rat and human demonstrated that fingolimod-P exposure was about 10- to 12-fold lower in human compared with rat for equivalent doses when following a dose-by-factor approach, which is commonly applied to scale the "no-observed adverse effect level" (Fig. 6) (Sharma and McNeill, 2009; FDA, 2010). This approach uses allometric scaling on the basis of body surface area. Generally, an exponent of 0.67 or 0.75 is used. For example, in rat a dose of 0.1 mg/kg results in an exposure of 1005 ng*h/ml. The human-equivalent dose after applying the dose-by-factor approach with an exponent of 0.75 equals 1.8 mg [0.1*70*(70/0.3)−0.25]. The “observed” exposure as predicted by the developed PK model for human was 95 ng*h/ml. As a result, there was an 11 (1005/95)-fold difference in exposure between rat and human.

Comparison of the predicted steady-state fingolimod-P exposures (AUCss) in blood after oral administration of fingolimod in doses of 0.1–5 mg/kg in rat and 0.1–5 mg in human. The dashed and continuous lines represent the exposure in rat and human, respectively.

Discussion

With the aim of 1) investigating whether characterization of the phosphorylation in blood platelets constitutes a basis for pharmacokinetic scaling and 2) simulating plasma rather than whole blood concentrations of fingolimod phosphate, PK models were developed to quantify the exposure of the prototypical S1PHK substrate fingolimod and its active metabolite fingolimod-P in rat and human. Previously, the time course of the blood concentrations of the parent compound but not the phosphorylated metabolite has been described by a physiologically based pharmacokinetic model (Meno-Tetang et al., 2006). In addition, the time course of the fingolimod-P blood concentrations has been described by a descriptive population PK model (Wu et al., 2012). However, to date, no pharmacokinetic models have been published that describe the time course of the fingolimod and fingolimod-P concentrations simultaneously.

The developed models, i.e., the rat model and the human model, consisted of three parts to describe the phosphorylation and the dephosphorylation in blood, the distribution and elimination from the systemic circulations, and the absorption, respectively. Although both models were structurally related, several differences are noticeable between the rat and human models. First of all, not all peripheral compartments that were identified in the rat model could be identified in the human model. This is explained by the fact that fingolimod (-P) concentrations were not measured after intravenous administration of fingolimod in human and, therefore, less detailed information was available about the distribution. Another important difference between the rat and human model is that saturable binding to a high affinity/low capacity binding site on a protein in the plasma was identified in humans, whereas this could not be identified in rats. This could represent saturable binding to high-density lipoprotein, because in human plasma, more than half of S1P is found in the high-density lipoprotein fraction (Obinata and Hla, 2012) and S1P and fingolimod-P are structurally related. As a result, the fingolimod-P blood/plasma exposure ratio was constant over the observed dose range (the ratio was about 1) in rats, whereas this ratio increased with higher doses from 0.95 for a dose of 0.5 mg to 1.9 for a dose of 5 mg at steady state in human. Therefore, the human plasma concentrations may be a little higher than anticipated after administration of doses below 0.5 mg/day In addition, for a dose of 0.5 mg/day the blood/plasma concentration ratio varied between 0.8 and 0.95 within a day at steady state (Fig. 5). The difference between blood and plasma concentrations is the largest around the time at which the maximum plasma concentration is reached. This is relevant because the fingolimod-P plasma concentrations are likely to be more predictive for pharmacodynamic effects than blood concentrations. Finally, in both species, the in vivo dephosphorylation was found to be much faster than the dephosphorylation in isolated blood. Fingolimod-P is dephosphorylated by lipid phosphatase type 3, which is expressed on cells exposed to plasma such as vascular endothelial cells, which are not present in the isolated blood used for the ex vivo studies. In humans, dephosphorylation is best described by a Michaelis-Menten process; whereas in rats no capacity limited (Michelis-Menten) kinetics could be identified because of the limited concentration range that has been studied. The developed models are valid in the evaluated dose range of 0.1 to 3 mg/kg after oral administration in rat and 0.5 to 5 mg after oral once daily administration to humans. In general, the data from the studies in rat and human were adequately described. However, in study 2105, the observations from the 1.25 mg–dose group were slightly overpredicted. This is thought to be due to noncompliance for some subjects in this treatment group. In addition, for this study, the variability was slightly overpredicted. Because there were only 12 subjects per treatment group included in this study the observed variability may not be representative for the variability in a larger population. An external validation of the human model using data from a single-dose study with doses between 5 and 40 mg demonstrated that the model can also be used to simulate fingolimod (-P) blood concentrations after doses up to 10 mg, which is a dose well above the therapeutic dose of 0.5 mg once daily. The developed models can be applied to evaluate possible covariate influences or to simulate the time course of the fingolimod and fingolimod-P plasma concentrations. Moreover, the model can be applied to characterize the time course of pharmacodynamic effects of fingolimod-P by linking the time course of the fingolimod-P plasma or blood concentrations to pharmacodynamic observations.

Various dose extrapolation techniques have been described ranging from empirical allometric scaling to semimechanistic methodologies, which attempt to account for species difference in physiology, and further to the mechanistic whole-body PBPK modeling approach, which relies on physicochemical properties of the drug and knowledge of physiology (tissue composition)(Jones et al., 2011). When applying a dose-by-factor approach, which uses allometric scaling on the basis of body surface area, the exposure of fingolimod-P in human was 10- to 12-fold overpredicted. It is generally accepted that an allometric scaling approach is not applicable when there are differences in metabolism between species. However, quantitatively understanding the differences in metabolism, i.e., interconversion, could constitute a basis for interspecies scaling. When examining the interconversion rate parameters in both species it is noticeable that the phosphorylation of fingolimod in the platelets is fourfold faster in rats compared with humans after allometric scaling using an exponent of −0.25 (West et al., 1999) (Table 2, k67). As in rats, an extra phosphorylation rate was estimated in the plasma, the overall phosphorylation was ninefold faster in rats compared with humans. This extra phosphorylation could represent rapid phosphorylation in other tissues, but this rate was not quantifiable in human. This could possibly be due to differences in the S1PHK2 enzyme tissue distribution, which may also explain the inadequate allometric prediction of the volume of distribution as interspecies differences in interconversion are not accounted for in a general allometric scaling approach. Overall, the fourfold difference in phosphorylation rate quantified from the ex vivo experiments is indicative for differences in exposure between rat and human but does not exclusively elucidate this difference. This is explained by the minor contribution of phosporylation in the platelets compared with the 82 and 69% presystemic phosphorylation seen in rats and humans, respectively. More mechanistic approaches are required to integrate the differences in presystemic phosphorylation and enzyme tissue distribution in the translational pharmacokinetics of fingolimod and fingolimod-P and other S1PHK substrates. For example, a PBPK modeling approach may be applied that uses two PBPK models, one for fingolimod and one for fingolimod-P, that are linked by phosphorylation and dephosphorylation processes

In conclusion, large interspecies differences in the rate of phosphorylation between rats and humans were demonstrated, using fingolimod as a model compound, which cannot be accounted for by allometric scaling. A semimechanistic PK model is proposed that constitutes a basis for the prediction of the concentrations of S1PHK substrates and their phosphorylated metabolites in plasma. In this model, differences in the rate of phosphorylation in blood, estimated from ex vivo interconversion measurements in platelets, partly explain the differences in exposure between rats and humans. However, differences in presystemic phosphorylation should also be taken into account.

Because not all parameters could be estimated independently, the following parameters were set equal: k36 = k67; k48 = k311; k84 = k113; VM410 = VM39; KM410 = KM39; k104 = k113. In addition, the hematocrit was fixed to 0.465.

Because not all parameters could be estimated independently the following parameters were set equal: k36 = k67; k47 = k74; k48 = VM43. In addition, kaSTD2105 was fixed to 9, and the hematocrit was fixed to 0.45.

Furthermore, for the ex vivo experiments the following parameters were fixed to 0: k30, k48, and k84.

The measurements of the in vivo studies were predicted according to eqs. A2.11 and A2.12, where IPRED represents the individual model prediction.

(A2.11)(A2.12)

In addition, the measurements of the ex vivo studies were predicted according to eqs. A2.13 to A2.17.

(A2.13)(A2.14)(A2.15)(A2.16)(A2.17)

Appendix 3:

Sensitivity Analysis

In this investigation, a semimechanistic pharmacokinetic model for the interconversion of S1PHK substrates and their respective phosphates in rats and humans was presented with the aim of investigating whether characterization of the rate of phosphorylation in blood platelets constitutes a basis for interspecies scaling using fingolimod as a model compound. The rate of phosphorylation was quantified by simultaneous analysis of the in vivo concentration-time course of fingolimod and fingolimod-P and the ex vivo interconversion and blood-plasma distribution. By showing how the dynamic behavior of the system responds to changes in parameter values, a sensitivity analysis provides the information on whether the data contain information to distinguish one parameter from another. By using the parameter estimates of the developed model, a retrospective parameter sensitivity analysis was performed in Berkeley Madonna (version 8.3.18, Berkeley Madonna Inc., University of California, Berkeley, CA) to determine how “sensitive” the developed model is to changes in the values of the parameters of the model.

First a simulation was performed with all system parameters fixed at their estimated values [S(t,x0)]. Subsequently, simulations were performed after 0.1% increments in the system parameters (0.1% is the standard in Berkeley Madonna) [S(t,x)]. Finally, for each parameter, the sensitivity [S(t)] was calculated according to eq. A3.1.

(A3.1)

The sensitivity [S(t)] in fingolimod and fingolimod-P concentrations was evaluated for all blood-specific parameters of the rat model after hypothetical oral administration of fingolimod in a dose of 1 mg/kg (Fig. 7). This figure shows that the fingolimod measurements are especially informative for estimation of k67 and k63, whereas the fingolimiod-P measurements are informative for estimation of k67, k63, and k74. However, the model simulations are relatively insensitive to changes k43. This means that the data after oral administration of fingolimod and fingolimod-P are not informative for estimation of k43. However, the model was optimized using data from in vivo and ex vivo studies. The data from the ex vivo studies was informative for estimation of k43 as demonstrated in an additional sensitivity analysis where the sensitivity in fingolimod and fingolimod-P blood concentrations, according to the experimental design of ex vivo experiment A, and in plasma, according to the experimental design of ex vivo experiment B, was evaluated for all blood-specific parameters of the rat model after hypothetical spiking of blood with fingolimod-P at a concentration of 30 ng/ml (Fig. 8). In addition, the data from study 2, in which fingolimod and fingolimod-P where administered intravenously, were informative for all four blood-specific parameters (results not shown).

Sensitivity analysis in vivo studies. Influence of a 0.1% increase in the values of the blood-specific parameters of the rat model (k74, k67, k63, and k43) on the time course of the fingolimod and fingolimod-P blood concentrations. In this sensitivity analysis, an oral administration of 1 mg/kg fingolimod was simulated.

Sensitivity analysis ex vivo studies. Influence of a 0.1% increase in the values of the blood-specific parameters of the rat model (k74, k67, k63, and k43) on the time course of the fingolimod and fingolimod-P blood or plasma concentrations according to the experimental designs of the ex vivo experiments A and B. In this sensitivity analysis, blood was spiked with 30 ng/ml fingolimod-P in both experiments.

References

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